Download Factor and Solve Polynomial Equations

Factor and Solve Polynomial
Equations
2.3 (GREEN book)
Vocabulary

A factorable polynomial with integer
coefficients is factored completely if it is
written as a product of unfactorable
polynomials with integer coefficients.
Factoring Quadratic Equations
I.
II.
GCF - Always!!
2 Terms
A. Difference of Squares a2 – b2 = _____________________________
B. Sum of Cubes
a3 + b3 = _____________________________
C. Difference of Cubes
a3 – b3 = ____________________________
III. 3 Terms
A. Trinomial Square
a.
a2 + 2ab + b2 = __________________________
b.
a2 – 2ab + b2 = __________________________
B. Plain Trinomial
a.
x2 + bx + c ___________________
b. ax2 + bx + c ___________________________
IV.
4 Terms - Grouping
Vocabulary

For some polynomials you can factor by grouping
pairs of terms that have a common monomial factor.
y  7 y  9 y  63
3
2
Example 1:
1.
Factor the polynomial completely
4x4 – 108x
2.
2b3 + 16a3

Example 2:

Factor the polynomial x3 + 2x2 – x – 2
completely.
Example 3:
1.
Factor completely:
3x8 + 18x5 + 24x2
2.
81g4 - 256

Example 4:

Find the real-number solutions of the
equation x4 – 7x2 = -12
Example 5.

The dimensions (in inches) of a jewelry box are:
length 4x, width (x – 1), and height (x – 2). If the
volume of the box is 24 cubic inches, find the
dimensions of the box.